This is a good example of a repair we did on a "popcorn" ceiling that had become water damaged due to a couple of old leaky skylights. As you click across the pictures you will notice the "before and after" shots.
This repair involves scraping off the damaged drywall and "popcorn", re-taping and mudding the damaged area and then using a spatter gun to "blow" on the new texture. This sort of repair is a real challenge when you are trying to match the existing ceiling and should only be attempted by an experienced technician.